アイスクリーム統計学・第４章〜第６章.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# アイスクリーム統計学 + Python (第４章〜第６章)\n",
    "\n",
    "* [アイスクリーム統計学・第１章〜第３章（散布図と相関、相関係数、無相関検定）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%93%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第４章〜第６章（単回帰、偏相関、重回帰）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%94%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%96%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第７章〜第９章（相関行列、因子分析1、因子分析2）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%97%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%99%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第１０章（主成分分析とクラスター分析）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%EF%BC%90%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第１１章（分布と仮説検定）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%EF%BC%91%E7%AB%A0.ipynb)\n",
    "\n",
    "[アイスクリーム統計学にようこそ！](http://kogolab.chillout.jp/elearn/icecream/index.html)\n",
    "のページを読み進めながら、以下の課題を Python を使って解いてください。\n",
    "\n",
    "### Jupyter Notebook (IPython Notebook) とは\n",
    "* Python という名のプログラミング言語が使えるプログラミング環境。計算コードと計算結果を同じ場所に時系列で保存できるので、実験系における実験ノートのように、いつどんな処理を行って何を得たのか記録して再現するのに便利。\n",
    "* [当学演習室での Jupyter Notebook の起動方法](https://raw.githubusercontent.com/maskot1977/-/master/%E6%BC%94%E7%BF%92%E5%AE%A4.txt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.　[単回帰](http://kogolab.chillout.jp/elearn/icecream/chap4/sec0.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1　[散布図に線を引く](http://kogolab.chillout.jp/elearn/icecream/chap4/sec1.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題4.1__　[去年の夏](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream2.txt)をダウンロードし、散布図を描いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# URL によるリソースへのアクセスを提供するライブラリをインポートする。\n",
    "import urllib # Python 2 の場合\n",
    "# import urllib.request # Python 3 の場合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ウェブ上のリソースを指定する\n",
    "url = 'https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream2.txt'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('ice_cream2.txt', <httplib.HTTPMessage instance at 0x10411ae18>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 指定したURLからリソースをダウンロードし、名前をつける。\n",
    "urllib.urlretrieve(url, 'ice_cream2.txt') # Python 2 の場合\n",
    "# urllib.request.urlretrieve(url, 'ice_cream.txt') # Python 3 の場合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ダウンロードしたデータから、列ごとに数字を読み込んでリストに格納する。\n",
    "col1 = []\n",
    "col2 = []\n",
    "col3 = []\n",
    "for i, line in enumerate(open('ice_cream2.txt')):\n",
    "    if i == 0:\n",
    "        continue\n",
    "    a = line.split()\n",
    "    col1.append(int(a[0]))\n",
    "    col2.append(int(a[1]))\n",
    "    col3.append(int(a[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 図やグラフを図示するためのライブラリをインポートする。\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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y1FNPUa9ePQAKCgooKiqiXbt2TJ48Oe5xxFPcelwraO/6a6Cdmd0tqRXQ3Mzm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c70c810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(col2, col3, alpha=0.5)\n",
    "plt.title(\"Numbers of customers in last summer\")\n",
    "plt.xlabel(\"Temperature\")\n",
    "plt.ylabel(\"Customers\")\n",
    "for day, x, y in zip(col1, col2, col3):\n",
    "    plt.text(x, y, day, alpha=0.8, size=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2　[回帰直線の原理](http://kogolab.chillout.jp/elearn/icecream/chap4/sec2.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3　[回帰直線を求める](http://kogolab.chillout.jp/elearn/icecream/chap4/sec3.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4　[回帰直線を求めてみよう](http://kogolab.chillout.jp/elearn/icecream/chap4/sec4.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題4.4__：　[去年の夏](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream2.txt)をダウンロードし、以下の問に答えてください。\n",
    "* 相関係数を求めてください。\n",
    "    * 相関係数＝偏差積の平均／（xの標準偏差＊yの標準偏差）\n",
    "* 回帰直線の傾きを求めてください。\n",
    "    * 回帰直線の傾き＝相関係数＊（（yの標準偏差）／（xの標準偏差））\n",
    "* 回帰直線のy切片を求めてください。\n",
    "* 散布図に回帰直線を描き入れてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 平均値を求める関数\n",
    "def average(list):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分散を求める関数\n",
    "def variance(list):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 標準偏差を求める関数\n",
    "def standard_deviation(list):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 共分散 = 偏差積の平均 （偏差値、ではありません。偏差積、です）\n",
    "def covariance(list1, list2):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 相関係数 = 偏差積の平均をX, Yの標準偏差で割ったもの\n",
    "def correlation(list1, list2):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8703518769354424"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 相関係数を求める\n",
    "correlation(col2, col3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 回帰直線の傾き＝相関係数＊（（yの標準偏差）／（xの標準偏差））を求める関数\n",
    "def a_fit(xlist, ylist):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# y切片＝yの平均－（傾き＊xの平均）を求める関数\n",
    "def b_fit(xlist, ylist):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = ax + b; (a, b) = (17.2482570476, -229.981812671)\n"
     ]
    }
   ],
   "source": [
    "# 回帰直線の式\n",
    "print(\"y = ax + b; (a, b) = ({0}, {1})\".format(a_fit(col2, col3), b_fit(col2, col3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 回帰直線を描くための準備\n",
    "fitted_y = []\n",
    "for x in col2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YiIgIt8TgTlrJV3O+Mn+2r9M8Wae5KlvJV6hCj1JfBrNt2zYaN25Mx44dOXfu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\nm5mZ1SgXeTMzsxr1/76LE5c5BvfoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f084e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 散布図と回帰直線を描く。\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.plot(col2,col3,'bo', label='Exp.')\n",
    "plt.plot(col2,fitted_y,'k-', label='fitted line', linewidth=10, alpha=0.3)\n",
    "plt.title(\"Numbers of customers in last summer\")\n",
    "plt.xlabel(\"Temperature\")\n",
    "plt.ylabel(\"Customers\")\n",
    "plt.legend(loc='best',fancybox=True, shadow=True)\n",
    "plt.grid(True)\n",
    "for day, x, y in zip(col1, col2, col3):\n",
    "    plt.text(x, y, day, alpha=0.8, size=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5　[（応用編）回帰直線で予測する](http://kogolab.chillout.jp/elearn/icecream/chap4/sec5.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題4.5__：[店舗別８月の平均客数データ（12店舗）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/shop_distance.txt)をダウンロードし、相関係数、回帰直線の傾き、回帰直線のy切片を求め、散布図に回帰直線を描き入れてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ダウンロードしたデータから、列ごとに数字を読み込んでリストに格納する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 相関係数を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線の式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線を描くための準備"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 散布図と回帰直線を描く。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6　[通過テスト](http://kogolab.chillout.jp/elearn/icecream/chap4/sec6.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題4.6__：[入学試験の点数と学業成績](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/entrance_exam.txt)のデータを用いて、以下の問いに答えてください。\n",
    "* 相関係数、回帰直線の傾き、回帰直線のy切片を求め、散布図に回帰直線を描き入れてください。\n",
    "* その回帰直線を使って、入学試験の点数が、400点、500点、600点、700点のときのそれぞれの学業成績の予測値を求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ダウンロードしたデータから、列ごとに数字を読み込んでリストに格納する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 相関係数を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線の式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線を描くための準備"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 散布図と回帰直線を描く。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.　[偏相関](http://kogolab.chillout.jp/elearn/icecream/chap5/sec0.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1　[もうひとつの相関](http://kogolab.chillout.jp/elearn/icecream/chap5/sec1.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題5.1__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用い、次の問いに答えてください。\n",
    "* 最低気温と客数の関係について、相関係数、回帰直線の傾き、回帰直線のy切片を求め、散布図に回帰直線を描き入れてください。\n",
    "* 有意な相関といえるかどうか考察してください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ダウンロードしたデータから、列ごとに数字を読み込んでリストに格納する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 相関係数を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線の式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線を描くための準備"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 散布図と回帰直線を描く。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2　[偏相関とは](http://kogolab.chillout.jp/elearn/icecream/chap5/sec2.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3　[偏相関係数を求める](http://kogolab.chillout.jp/elearn/icecream/chap5/sec3.html)\n",
    "* a の影響を除いた、b と y の偏相関係数 = （__r__<sub>by</sub> - (__r__<sub>ay</sub> ＊ __r__<sub>ab</sub>)) / sqrt ((1 - __r__<sub>ay</sub><sup>2</sup>) ＊ (1 - __r__<sub>ab</sub><sup>2</sup>))\n",
    "\n",
    "__課題5.3__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用い、最高気温の影響を取り除いた、最低気温と客数の偏相関係数を求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ダウンロードしたデータから、列ごとに数字を読み込んでリストに格納する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# a の影響を除いた、b と y の偏相関係数 partial correlation coefficient を求める関数\n",
    "def partial_correlation(a, b, y):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.895600384086399"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partial_correlation(col2, col3, col4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4　[もうひとつの偏相関係数](http://kogolab.chillout.jp/elearn/icecream/chap5/sec4.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題5.4__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用い、最低気温の影響を取り除いた、最高気温と客数の偏相関係数を求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9732414179952071"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.5　[偏相関再び](http://kogolab.chillout.jp/elearn/icecream/chap5/sec5.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.6　[通過テスト](http://kogolab.chillout.jp/elearn/icecream/chap5/sec6.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題5.6__：[入学試験の点数と学業成績（高校の平均評定込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/entrance_exam2.txt)のデータを用い、以下の問いに答えてください。\n",
    "* 高校の平均評点（10点満点）、入学試験の点数、入学後の学業成績（GPA：4点満点）の、３種類のデータのすべての組み合わせの相関係数を求めてください。\n",
    "* 高校の平均評定の影響を取り除いたときの、入学試験の点数と入学後の学業成績の偏相関係数を求めてください。\n",
    "* 入学試験の点数と入学後の学業成績の偏相関係数について、考えられる解釈を文章で書いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.　[重回帰](http://kogolab.chillout.jp/elearn/icecream/chap6/sec0.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1　[偏回帰係数](http://kogolab.chillout.jp/elearn/icecream/chap6/sec1.html)\n",
    "* a の影響を除いた、b と y の偏回帰係数 = （__r__<sub>by</sub> - (__r__<sub>ay</sub> ＊ __r__<sub>ab</sub>)) ＊ __σ__<sub>y</sub> /  ((1 - __r__<sub>ab</sub><sup>2</sup>) ＊ __σ__<sub>b</sub>)\n",
    "* a の影響を除いた、b と y の標準偏回帰係数 = （__r__<sub>by</sub> - (__r__<sub>ay</sub> ＊ __r__<sub>ab</sub>)) /  (1 - __r__<sub>ab</sub><sup>2</sup>)\n",
    "\n",
    "__課題6.1__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用いて以下の問いに答えてください。\n",
    "* 最高気温の影響を取り除いた、最低気温と客数の偏回帰係数を求めてください。\n",
    "* 最高気温の影響を取り除いた、最低気温と客数の標準偏回帰係数を求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# a の影響を除いた、b と y の偏相関係数 partial regression coefficient を求める関数\n",
    "def partial_regression(a, b, y):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-16.703141150412772"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partial_regression(col2, col3, col4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# a の影響を除いた、b と y の標準偏相関係数 standard partial regression coefficient を求める関数\n",
    "def standard_partial_regression(a, b, y):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6225767534015739"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "standard_partial_regression(col2, col3, col4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2　[２つの変数で予測する](http://kogolab.chillout.jp/elearn/icecream/chap6/sec2.html)\n",
    "本文を読んで概念を学んでください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3　[重回帰モデル](http://kogolab.chillout.jp/elearn/icecream/chap6/sec3.html)\n",
    "__課題6.3__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用い、「客数の予測値　＝　定数m　＋　定数p × 最高気温　＋　定数q × 最低気温」という重回帰モデルを考えたときの、定数m, p, qを求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4　[重回帰モデルによる予測](http://kogolab.chillout.jp/elearn/icecream/chap6/sec4.html)\n",
    "__課題6.4__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用い、「客数の予測値　＝　定数m　＋　定数p × 最高気温　＋　定数q × 最低気温」という重回帰モデルを考えたときの、重回帰モデルによる予測値と実際の客数との相関係数を求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.5　[重相関係数](http://kogolab.chillout.jp/elearn/icecream/chap6/sec5.html)\n",
    "実測値と重回帰モデルによる予測値の相関係数を「重相関係数」(Multiple correlation coefficient)と呼ぶ。\n",
    "* sqrt( (__r__<sub>ay</sub><sup>2</sup> + __r__<sub>by</sub><sup>2</sup> - 2 ＊ __r__<sub>ay</sub> ＊ __r__<sub>by</sub> ＊ __r__<sub>ab</sub>) / (1 -  __r__<sub>ab</sub><sup>2</sup>) )\n",
    "\n",
    "__課題6.5__：[去年の夏（最低気温込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/ice_cream3.txt)のデータを用い、最高気温と最低気温から客数を予測する場合の重相関係数を求めてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.6　[通過テスト](http://kogolab.chillout.jp/elearn/icecream/chap6/sec6.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題6.6__：[入学試験の点数と学業成績（高校の平均評定込み）](https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/entrance_exam2.txt)のデータを用いて、以下の問いに答えてください。\n",
    "* 入学後の学業成績を、高校の平均評点と入学試験の点数の２つの変数を使って、重回帰モデルによって予測したい。このときのモデルの式を書いてください。\n",
    "* その重回帰モデルの式における定数を求めてください。\n",
    "* その重回帰モデルにおける重相関係数を求めてください。\n",
    "* 入学試験と学業成績の相関係数と、重相関係数とを比較して、どのようなことが言えるかについて、文章で書いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__今日の課題提出__：計算結果を.ipynb ファイル（または.jsonファイル）として保存し、指定したアドレスまでメールしてください。メールタイトルは「__アイスクリーム統計学４５６__」とし、メール本文に学籍番号と氏名を明記のこと。また、感想も書いてくれると喜びます。今後の講義の改善につながるかも知れません。"
   ]
  }
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